Finite Group Databasebeta

#101×D491 #44536703

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

Aliases

direct product#101×D491

Splittings

Fitting#101×C491 ⋊ C2
SylowC491 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D491
commutatorC22×C491C22×C4
FrattiniC2×C4C22×D491
Fitting#101×C491C2
socleC2×C491C2×C22⋊C4
prime radicalC22×D491C2×C4
cosocleC2×C4×C491C23
hypercenter#101D491
hypocenterC491C2×#101
LCSG ▷ C22×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7856

Conjugacy classes & character table

2717 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 527);