Finite Group Databasebeta

#108×D229 #28411525

order14656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D229

Splittings

Fitting#108×C229 ⋊ C2
SylowC229 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D229
commutatorC4×C229C22×C4
FrattiniC2×C4C22×D229
Fitting#108×C229C2
socleC2×C229C2×C4⋊C4
prime radicalC22×D229Q8
cosocleC2×C4×C229C23
hypercenter#108D229
hypocenterC229C2×#108
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3664

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 593);