Finite Group Databasebeta

#107×#3633 #17981633

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

Aliases

direct product#107×#3633

Splittings

FittingC17×#107 ⋊ C8
SylowC17 ⋊ C8×#107

Subgroups

subgroupG/H
centerC22D4×#3633
commutatorC4×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC17×#107C8
socleC22×C17C8×D4
prime radicalC22×D17C4×D4
cosocleC2×C4×#595C23
hypercenter#107#3633
hypocenterC17C8×#107
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116877);