Finite Group Databasebeta

C2×Dic2824 #36378215

order22592
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic2824

Splittings

SylowC353 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D2824
commutator, cosocleC8×C353C23
FrattiniC8C22×D353
FittingC2×C16×C353C2
socle, prime radicalC22×C353D8
hypercenterC2×C16D353
hypocenterC353C2×Q32
LCSG ▷ C8×C353 ▷ C4×C353 ▷ C2×C353 ▷ C353
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22592

Conjugacy classes & character table

5654 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22592, 977);