C₁₃⋊C₃×C₇⋊#1035 #41031203

order	27300
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇×C₁₃×C₂₅	C₃×C₄
Frattini	C₅	C₁₃⋊C₃×C₇⋊AGL(1,𝔽₅)
socle	C₅×C₇×C₁₃	C₃×AGL(1,𝔽₅)
prime radical	C₇×C₁₃⋊C₃×D₂₅	C₂
cosocle	C₇×C₁₃×D₂₅	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₂₅
UCS	C₁

72 conjugacy classes of subgroups.

μ_t(G) = 2275

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 93);