Finite Group Databasebeta

C4×#11763610 #17898537

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#11763610

Splittings

FittingC2×C4×D8×C17 ⋊ C2
SylowC17 ⋊ C4×#576

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C4×D8×C17C2
socleC22×C17C23×D4
prime radicalC2×#11763610C2
cosocleC2×C4×C17C25
hypercenterC2×C4×D8D17
hypocenterC17C4×#576
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D8

2826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033781);