Finite Group Databasebeta

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C2×C4×#13063264 #25249225

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#13063264

Splittings

FittingC2×C4×C16×C43 ⋊ C2
SylowC43 ⋊ C2×C4×M32

Subgroups

subgroupG/H
centerC2×C4×C8C2×D43
commutatorC2×C43C22×C4×C8
FrattiniC2×C8C23×D43
FittingC2×C4×C16×C43C2
socleC23×C43C22×C8
prime radicalC23×D43C2×C8
cosocleC2×C8×C43C24
hypercenterC2×C4×C16D43
hypocenterC43C2×C4×M32
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

918 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322196);