Finite Group Databasebeta

C4×C4⋊C8×D17 #17032193

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C4⋊C8×D17

Splittings

FittingC4×C17×C4⋊C8 ⋊ C2
SylowC17 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC2×C17C22×C4×C8
FrattiniC22×C4C23×D17
FittingC4×C17×C4⋊C8C2
socleC23×C17C23×C4
prime radicalC23×D17C22×C4
cosocleC22×C4×C17C24
hypercenterC4×C4⋊C8D17
hypocenterC17C2×C4×C4⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167437);