Finite Group Databasebeta

#107×#3624 #17952347

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#107×#3624

Splittings

SylowC17 ⋊ C8×#107

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC4×C17C2×C4×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#107C4
socle, prime radicalC23×C17C4×D4
cosocleC2×C4×Dic17C23
hypercenterC2×#107#595
hypocenterC17C8×#107
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 1087591);