Finite Group Databasebeta

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C2×#19133084 #25063689

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19133084

Splittings

FittingC2×C4×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×#1501

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×C22⋊C4×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×#1501
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1606 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, 136660);