Finite Group Databasebeta

#107×D421 #41002872

order26944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#107×D421

Splittings

Fitting#107×C421 ⋊ C2
SylowC421 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D421
commutatorC4×C421C22×C4
FrattiniC2×C4C22×D421
Fitting#107×C421C2
socleC22×C421C2×D4
prime radicalC22×D421D4
cosocleC2×C4×C421C23
hypercenter#107D421
hypocenterC421C2×#107
LCSG ▷ C4×C421 ▷ C2×C421 ▷ C421
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

2968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 581);