Finite Group Databasebeta

C2×#29504547 #44486137

order30592
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#29504547

Splittings

SylowC239 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D239
commutatorC2×C239C2×C4×C8
FrattiniC2×C8C22×D239
FittingC22×C16×C239C2
socle, prime radicalC23×C239C2×C8
cosocleC2×C8×C239C23
hypercenterC22×C16D239
hypocenterC239C2×#346
LCSG ▷ C2×C239 ▷ C239
UCSC1 ◁ C22×C8 ◁ C22×C16

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

7696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6099);