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C₂²×#20263540 #38760922

order	25308
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂²×#20263540

Splittings

derived, Hall	C₁₉×C₃₇ ⋊ C₂²×C₉
Hall	C₂²×C₁₉×C₃₇ ⋊ C₉
Hall	C₂²×C₃₇ ⋊ #4294
Hall	C₂²×C₁₉ ⋊ #66524
Sylow	C₃₇ ⋊ C₂²×#4294
Sylow	C₁₉ ⋊ C₂²×#66524

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃	#14523722
commutator, hypocenter	C₁₉×C₃₇	C₂²×C₉
Frattini	C₃	C₂²×#14523722
Fitting, socle	C₂²×C₃×C₁₉×C₃₇	C₃
LCS	G ▷ C₁₉×C₃₇
UCS	C₁ ◁ C₂²×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 66);