Finite Group Databasebeta

#108×#3624 #17952391

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct product#108×#3624

Splittings

SylowC17 ⋊ C8×#108

Subgroups

subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C2×C4×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#108C4
socleC22×C17C4×C4⋊C4
prime radicalC23×C17C4×Q8
cosocleC2×C4×Dic17C23
hypercenterC2×#108#595
hypocenterC17C8×#108
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1087635);