Finite Group Databasebeta

← Prev (#44509997) Next (#44509999) →

C4×#21440637 #44509998

order30848
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#21440637

Splittings

FittingC4×C4⋊C4×C241 ⋊ C2
SylowC241 ⋊ C4×#126

Subgroups

subgroupG/H
centerC22×C4C22×D241
commutatorC22×C241C23×C4
FrattiniC23C23×D241
FittingC4×C4⋊C4×C241C2
socle, cosocleC23×C241C24
prime radicalC23×D241C23
hypercenterC4×C4⋊C4D241
hypocenterC241C4×#126
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

Conjugacy classes & character table

4856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 7063);