Finite Group Databasebeta

#107×D457 #44416809

order29248
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#107×D457

Splittings

Fitting#107×C457 ⋊ C2
SylowC457 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D457
commutatorC4×C457C22×C4
FrattiniC2×C4C22×D457
Fitting#107×C457C2
socleC22×C457C2×D4
prime radicalC22×D457D4
cosocleC2×C4×C457C23
hypercenter#107D457
hypocenterC457C2×#107
LCSG ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14624

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 581);