Finite Group Databasebeta

C2×C4×(C2×D239)⋊C4 #44486879

order30592
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D239)⋊C4

Splittings

FittingC22×C42×C239 ⋊ C2
SylowC239 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D239
commutatorC2×C239C22×C42
FrattiniC23C23×D239
FittingC22×C42×C239C2
socleC24×C239C23
prime radicalC24×D239C22
cosocleC23×C239C24
hypercenterC22×C42D239
hypocenterC239C2×C4×C22⋊C4
LCSG ▷ C2×C239 ▷ C239
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15296

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, 6841);