Finite Group Databasebeta

C2×Dic2848 #36475478

order22784
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic2848

Splittings

SylowC89 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22D2848
commutator, cosocleC32×C89C23
FrattiniC32C22×D89
FittingC2×C64×C89C2
socle, prime radicalC22×C89D32
hypercenterC2×C64D89
hypocenterC89C2×Q128
LCSG ▷ C32×C89 ▷ C16×C89 ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

5702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 90618);