Finite Group Databasebeta

C2×#19132678 #25011455

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132678

Splittings

SylowC43 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC22×C43C2×C4×C8
FrattiniC22×C8C22×D43
FittingC22×M32×C43C2
socleC23×C43C22⋊C8
prime radicalC24×C43C2×C8
cosocleC22×C8×C43C23
hypercenterC22×M32D43
hypocenterC43C2×#1377
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×M32

630 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84426);