Finite Group Databasebeta

#108×D389 #38734143

order24896
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D389

Splittings

Fitting#108×C389 ⋊ C2
SylowC389 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D389
commutatorC4×C389C22×C4
FrattiniC2×C4C22×D389
Fitting#108×C389C2
socleC2×C389C2×C4⋊C4
prime radicalC22×D389Q8
cosocleC2×C4×C389C23
hypercenter#108D389
hypocenterC389C2×#108
LCSG ▷ C4×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6224

Conjugacy classes & character table

2744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 593);