Finite Group Databasebeta

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C2×#19132520 #25005665

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132520

Splittings

FittingC2×C43×C22⋊C16 ⋊ C2
SylowC43 ⋊ C2×#1315

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC2×C43×C22⋊C16C2
socleC23×C43C22⋊C8
prime radicalC22×#10621898C4
cosocleC22×C8×C43C23
hypercenterC2×C22⋊C16D43
hypocenterC43C2×#1315
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×C22⋊C16

534 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, 78636);