Finite Group Databasebeta

C2×#19145353 #25967123

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19145353

Splittings

FittingC22×C22⋊C8×C43 ⋊ C2
SylowC43 ⋊ C2×#3187

Subgroups

subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×C22⋊C8×C43C2
socleC23×C43C22×D4
prime radicalC22×#13063299C2
hypercenterC22×C22⋊C8D43
hypocenterC43C2×#3187
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

2698 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1040094);