C₂₃×Dic₂₅ #14556264

order	2300
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₃×Dic₂₅

Splittings

derived, Sylow	C₂₅ ⋊ C₄×C₂₃
Hall	C₂₃×C₂₅ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₂₅
commutator, hypocenter	C₂₅	C₄×C₂₃
Frattini	C₂×C₅	D₅×C₂₃
Fitting	C₂×C₂₃×C₂₅	C₂
socle, prime radical	C₂×C₅×C₂₃	D₅
cosocle	C₂×C₂₅	C₂×C₂₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₂₃

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 2300

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₂₃×Dic₂₅, C₂₃×Dic₁₇₅, C₂₃×#11744620, …
maximal normal subgroup of	C₇×C₂₃×Dic₂₅, C₁₁×C₂₃×Dic₂₅, Dic₂₅×C₂₃⋊C₁₁, …
maximal quotient of	C₇×C₂₃×Dic₂₅, C₂₃×Dic₁₇₅, C₂₃×#11744620, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2300, 2);

C23×Dic25 #14556264