Finite Group Databasebeta

#107×D41 #14580368

order2624
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#107×D41

Splittings

Fitting#107×C41 ⋊ C2
SylowC41 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D41
commutatorC4×C41C22×C4
FrattiniC2×C4C22×D41
Fitting#107×C41C2
socleC22×C41C2×D4
prime radicalC22×D41D4
cosocleC2×C4×C41C23
hypercenter#107D41
hypocenterC41C2×#107
LCSG ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 581);