Finite Group Databasebeta

C4×#16813558 #28390476

order14464
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16813558

Splittings

SylowC113 ⋊ C4×#108

Subgroups

subgroupG/H
centerC42D452
commutatorC4×C113C2×C42
FrattiniC22×C4C22×D113
FittingC2×C4×C8×C113C2
socleC22×C113C2×C4⋊C4
prime radicalC23×C113C2×Q8
cosocleC22×C4×C113C23
hypercenterC2×C4×C8D113
hypocenterC113C4×#108
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

3640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 4412);