Finite Group Databasebeta

#108×D463 #44444837

order29632
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D463

Splittings

Fitting#108×C463 ⋊ C2
SylowC463 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D463
commutatorC4×C463C22×C4
FrattiniC2×C4C22×D463
Fitting#108×C463C2
socleC2×C463C2×C4⋊C4
prime radicalC22×D463Q8
cosocleC2×C4×C463C23
hypercenter#108D463
hypocenterC463C2×#108
LCSG ▷ C4×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7408

Conjugacy classes & character table

3262 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 593);