Finite Group Databasebeta

#108×D491 #44536769

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

Aliases

direct product#108×D491

Splittings

Fitting#108×C491 ⋊ C2
SylowC491 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D491
commutatorC4×C491C22×C4
FrattiniC2×C4C22×D491
Fitting#108×C491C2
socleC2×C491C2×C4⋊C4
prime radicalC22×D491Q8
cosocleC2×C4×C491C23
hypercenter#108D491
hypocenterC491C2×#108
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7856

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, 593);