Finite Group Databasebeta

C2×Dic4184 #45690633

order33472
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic4184

Splittings

SylowC523 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D4184
commutator, cosocleC8×C523C23
FrattiniC8C22×D523
FittingC2×C16×C523C2
socle, prime radicalC22×C523D8
hypercenterC2×C16D523
hypocenterC523C2×Q32
LCSG ▷ C8×C523 ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33472

Conjugacy classes & character table

8374 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 977);