Finite Group Databasebeta

#107×D491 #44536757

order31424
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#107×D491

Splittings

Fitting#107×C491 ⋊ C2
SylowC491 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D491
commutatorC4×C491C22×C4
FrattiniC2×C4C22×D491
Fitting#107×C491C2
socleC22×C491C2×D4
prime radicalC22×D491D4
cosocleC2×C4×C491C23
hypercenter#107D491
hypocenterC491C2×#107
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

3458 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 581);