Finite Group Databasebeta

C2×#30660283 #45690153

order33472
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30660283

Splittings

SylowC523 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D523
commutatorC2×C523C2×C42
FrattiniC2×C4C22×D523
FittingC22×C8×C523C2
socle, prime radicalC23×C523C2×C4
cosocleC2×C4×C523C23
hypercenterC22×C8D523
hypocenterC523C2×#97
LCSG ▷ C2×C523 ▷ C523
UCSC1 ◁ C22×C4 ◁ C22×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33472

Conjugacy classes & character table

8392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 497);