Finite Group Databasebeta

C4×D17⋊#101 #17968386

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D17⋊#101

Splittings

SylowC17 ⋊ C2×C4×#101

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC23×D17C22×C4
cosocleC22×Dic17C24
hypercenterC2×C4×Q8#595
hypocenterC17C2×C4×#101
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

1538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103630);