Finite Group Databasebeta

← Prev (#44487382) Next (#44487384) →

C22⋊C4×Dic478 #44487383

order30592
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×Dic478

Splittings

SylowC239 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
FittingC4×C22⋊C4×C239C2
socle, cosocleC23×C239C24
prime radicalC24×C239C23
hypercenterC4×C22⋊C4D239
hypocenterC239Q8×C22⋊C4
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15296

Conjugacy classes & character table

4810 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 7345);