C₃×D₂₅×C₈₃ #27159477

order	12450
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₂₅×C₈₃
unambiguous semidirect product	C₂₅⋊(C₂×C₃×C₈₃)

Splittings

Fitting, Hall	C₃×C₂₅×C₈₃ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₃×C₈₃
Hall	C₂₅×C₈₃ ⋊ C₂×C₃
Hall	C₃×C₂₅ ⋊ C₂×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₈₃	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₃×C₈₃
Frattini	C₅	C₃×D₅×C₈₃
Fitting	C₃×C₂₅×C₈₃	C₂
socle	C₃×C₅×C₈₃	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃×C₈₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 111
transitive degree	μ_t(G) = 6225

A minimal faithful permutation representation — 2 generators on 111 points:

(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,18)(12,20)(14,22)(17,23)(19,24)(21,25)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108)(109,110,111);(1,6,21,20,4,3,14,24,10,9,8,23,18,11,17,16,15,5,19,22,7,2,12,25,13)

Conjugacy classes & character table

3486 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₈₃×#1035, C₃×C₈₃⋊#1035, C₃×D₂₅×D₈₃, …
maximal normal subgroup of	C₃×C₈₃×#1035, C₃×C₈₃⋊#1035, C₃×D₂₅×D₈₃, …
maximal quotient of	C₃×C₈₃×Dic₂₅, C₂×C₃×D₂₅×C₈₃, C₉×D₂₅×C₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12450, 3);

C3×D25×C83 #27159477