Finite Group Databasebeta

C2×C8×C4⋊#595 #17968521

order4352
isoclinismisoclinic class of #63243
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C8×C4⋊#595

Splittings

FittingC2×C4×C8×C17 ⋊ C4
SylowC17 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C8C2×#595
commutatorC2×C17C22×C4×C8
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC23×C17C2×C42
prime radicalC23×D17C22×C4
cosocleC2×C4×D17C24
hypercenterC2×C4×C8#595
hypocenterC17C2×C8×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103765);