Finite Group Databasebeta

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C₉×C₁₉×Dic₃₇ #38760862

order	25308
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×Dic₃₇

Splittings

derived, Sylow	C₃₇ ⋊ C₄×C₉×C₁₉
Hall	C₉×C₁₉×C₃₇ ⋊ C₄
Hall	C₁₉×C₃₇ ⋊ C₄×C₉
Hall	C₉×C₃₇ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₃₇
commutator, hypocenter	C₃₇	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₃×C₁₉×D₃₇
Fitting	C₂×C₉×C₁₉×C₃₇	C₂
socle	C₂×C₃×C₁₉×C₃₇	C₂×C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₉×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 6);