C₂₅×D₂₄₇ #27134693

order	12350
isoclinism	isoclinic class of D₂₄₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₅×D₂₄₇
unambiguous semidirect product	C₁₃⋊(C₂₅×D₁₉)
unambiguous semidirect product	C₁₉⋊(C₂₅×D₁₃)

Splittings

Fitting, Hall	C₁₃×C₁₉×C₂₅ ⋊ C₂
derived, Hall	C₁₃×C₁₉ ⋊ C₂×C₂₅
Hall	C₁₉×C₂₅ ⋊ D₁₃
Hall	C₁₃×C₂₅ ⋊ D₁₉
Sylow	C₁₉ ⋊ C₂₅×D₁₃
Sylow	C₁₃ ⋊ C₂₅×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₂₄₇
commutator, hypocenter	C₁₃×C₁₉	C₂×C₂₅
Frattini	C₅	C₅×D₂₄₇
Fitting	C₁₃×C₁₉×C₂₅	C₂
socle, cosocle	C₅×C₁₃×C₁₉	C₂×C₅
prime radical	C₅×D₂₄₇	C₅
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 6175

A minimal faithful permutation representation — 2 generators on 57 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34,36,39,43,35,37,40,44,48,38,41,45,49,52,42,46,50,53,55,47,51,54,56,57);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(20,21,23,25,27,29,31,32,30,28,26,24,22)

Conjugacy classes & character table

3125 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₅×D₁₃×D₁₉, D₂₅×D₂₄₇, D₂₄₇⋊D₂₅, …
maximal normal subgroup of	C₂₅×D₁₃×D₁₉, D₂₅×D₂₄₇, D₂₄₇⋊D₂₅, …
maximal quotient of	C₂₅×Dic₂₄₇, C₂×C₂₅×D₂₄₇, C₃×C₂₅×D₂₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12350, 4);

C25×D247 #27134693