Finite Group Databasebeta

#108×D523 #45690249

order33472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D523

Splittings

Fitting#108×C523 ⋊ C2
SylowC523 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D523
commutatorC4×C523C22×C4
FrattiniC2×C4C22×D523
Fitting#108×C523C2
socleC2×C523C2×C4⋊C4
prime radicalC22×D523Q8
cosocleC2×C4×C523C23
hypercenter#108D523
hypocenterC523C2×#108
LCSG ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8368

Conjugacy classes & character table

3682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 593);