Finite Group Databasebeta

#108×D461 #44442120

order29504
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D461

Splittings

Fitting#108×C461 ⋊ C2
SylowC461 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D461
commutatorC4×C461C22×C4
FrattiniC2×C4C22×D461
Fitting#108×C461C2
socleC2×C461C2×C4⋊C4
prime radicalC22×D461Q8
cosocleC2×C4×C461C23
hypercenter#108D461
hypocenterC461C2×#108
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7376

Conjugacy classes & character table

3248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 593);