Finite Group Databasebeta

#101×D359 #37526421

order22976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×D359

Splittings

Fitting#101×C359 ⋊ C2
SylowC359 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D359
commutatorC22×C359C22×C4
FrattiniC2×C4C22×D359
Fitting#101×C359C2
socleC2×C359C2×C22⋊C4
prime radicalC22×D359C2×C4
cosocleC2×C4×C359C23
hypercenter#101D359
hypocenterC359C2×#101
LCSG ▷ C22×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5744

Conjugacy classes & character table

1991 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 527);