Finite Group Databasebeta

#107×D68 #17052443

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#107×D68

Splittings

FittingC4×C17×#107 ⋊ C2
SylowC17 ⋊ D4×#107

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×#107C2
socleC23×C17C22×D4
prime radicalC22×D68D4
cosocleC22×C4×C17C24
hypercenterC4×#107D17
hypocenterC17D4×#107
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

1126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 187687);