Finite Group Databasebeta

C4×#22582815 #49095205

order35968
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#22582815

Splittings

SylowC281 ⋊ C4×#108

Subgroups

subgroupG/H
centerC42D1124
commutatorC4×C281C2×C42
FrattiniC22×C4C22×D281
FittingC2×C4×C8×C281C2
socleC22×C281C2×C4⋊C4
prime radicalC23×C281C2×Q8
cosocleC22×C4×C281C23
hypercenterC2×C4×C8D281
hypocenterC281C4×#108
LCSG ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

9016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 4412);