Finite Group Databasebeta

C2×#30660294 #45690192

order33472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#30660294

Splittings

SylowC523 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D523
commutatorC4×C523C22×C4
FrattiniC2×C4C22×D523
Fitting, prime radicalC22×D4×C523C2
socleC23×C523D4
cosocleC2×C4×C523C23
hypercenterC22×D4D523
hypocenterC523C2×#102
LCSG ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16736

Conjugacy classes & character table

5248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 536);