Finite Group Databasebeta

C2×#29504514 #44483132

order30592
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#29504514

Splittings

SylowC239 ⋊ C2×#330

Subgroups

subgroupG/H
centerC23C22⋊Dic239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
FittingC2×#125×C239C2
socle, prime radicalC23×C239C22⋊C4
cosocleC42×C239C23
hypercenterC2×#125D239
hypocenterC239C2×#330
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

3370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 3094);