Finite Group Databasebeta

C4×#11762616 #16949548

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11762616

Splittings

SylowC17 ⋊ C4×#359

Subgroups

subgroupG/H
centerC42#63228
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC4×C17×#135C2
socleC22×C17C2×#102
prime radicalC2×C17×#135C22
cosocleC22×C8×C17C23
hypercenterC4×#135D17
hypocenterC17C4×#359
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 84792);