Finite Group Databasebeta

C2×#19132638 #25007817

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132638

Splittings

SylowC43 ⋊ C2×#1360

Subgroups

subgroupG/H
centerC23#13063246
commutatorC2×C8×C43C22×C4
FrattiniC4×C8C22×D43
FittingC2×C43×#495C2
socleC23×C43#102
prime radicalC22×D8×C43C4
cosocleC4×C8×C43C23
hypercenterC2×#495D43
hypocenterC43C2×#1360
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#495

434 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 80788);