C₇×C₃₇×D₂₅ #27188307

order	12950
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₃₇×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂×C₇×C₃₇)

Splittings

Fitting, Hall	C₇×C₂₅×C₃₇ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₇×C₃₇
Hall	C₂₅×C₃₇ ⋊ C₂×C₇
Hall	C₇×C₂₅ ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₃₇	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₇×C₃₇
Frattini	C₅	C₇×D₅×C₃₇
Fitting	C₇×C₂₅×C₃₇	C₂
socle	C₅×C₇×C₃₇	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₇×C₃₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 6475

A minimal faithful permutation representation — 2 generators on 69 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);(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

3626 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₃₇×#1035, C₇×#16814856, C₃₇×C₇⋊#1035, …
maximal normal subgroup of	C₇×C₃₇×#1035, C₇×#16814856, C₃₇×C₇⋊#1035, …
maximal quotient of	C₇×C₃₇×Dic₂₅, C₂×C₇×C₃₇×D₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12950, 5);

C7×C37×D25 #27188307