Finite Group Databasebeta

C4×#11763062 #17040968

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11763062

Splittings

FittingC2×C4×M16×C17 ⋊ C2
SylowC17 ⋊ C4×#469

Subgroups

subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C4×M16×C17C2
socleC23×C17C22×D4
prime radicalC2×#11763062C2
cosocleC22×C4×C17C24
hypercenterC2×C4×M16D17
hypocenterC17C4×#469
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

1170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 176212);