Finite Group Databasebeta

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C₄×#14555735 #22580113

order	8892
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₄×#14555735

Splittings

derived, Hall	C₁₃×C₁₉ ⋊ C₄×C₉
Hall	C₄×C₁₃×C₁₉ ⋊ C₉
Hall	C₄×C₁₉ ⋊ C₁₃⋊C₉
Hall	C₄×C₁₃ ⋊ #4294
Sylow	C₁₉ ⋊ C₄×C₁₃⋊C₉
Sylow	C₁₃ ⋊ C₄×#4294

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄	#10625202
commutator, hypocenter	C₁₃×C₁₉	C₄×C₉
Frattini	C₂×C₃	C₂×#10625202
Fitting	C₃×C₄×C₁₃×C₁₉	C₃
socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃×C₄

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 16);