Finite Group Databasebeta

C2×#30660329 #45690658

order33472
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#30660329

Splittings

SylowC523 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D523
commutatorC2×C523C23×C4
FrattiniC22C23×D523
FittingC2×C22⋊C4×C523C2
socleC23×C523C23
prime radicalC24×C523C22
cosocleC22×C523C24
hypercenterC2×C22⋊C4D523
hypocenterC523C2×#117
LCSG ▷ C2×C523 ▷ C523
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16736

Conjugacy classes & character table

5260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 1002);