Finite Group Databasebeta

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C2×#19135166 #25098725

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19135166

Splittings

SylowC43 ⋊ C2×#1918

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×C4⋊C4×C43C2
socle, prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×#1918
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171696);