Finite Group Databasebeta

C4×#21439953 #44487097

order30592
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#21439953

Splittings

SylowC239 ⋊ C4×#126

Subgroups

subgroupG/H
centerC22×C4C22×D239
commutatorC22×C239C23×C4
FrattiniC23C23×D239
FittingC4×C22⋊C4×C239C2
socle, cosocleC23×C239C24
prime radicalC24×C239C23
hypercenterC4×C22⋊C4D239
hypocenterC239C4×#126
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15296

Conjugacy classes & character table

4816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 7059);