Finite Group Databasebeta

C2×#30660317 #45690629

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

Aliases

direct productC2×#30660317

Splittings

SylowC523 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#22552626
commutator, cosocleC8×C523C23
FrattiniC8C22×D523
Fitting, prime radicalC2×D8×C523C2
socleC22×C523D8
hypercenterC2×D8D523
hypocenterC523C2×SD32
LCSG ▷ C8×C523 ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16736

Conjugacy classes & character table

3676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 973);