Finite Group Databasebeta

#108×D593 #49182759

order37952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D593

Splittings

Fitting#108×C593 ⋊ C2
SylowC593 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D593
commutatorC4×C593C22×C4
FrattiniC2×C4C22×D593
Fitting#108×C593C2
socleC2×C593C2×C4⋊C4
prime radicalC22×D593Q8
cosocleC2×C4×C593C23
hypercenter#108D593
hypocenterC593C2×#108
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9488

Conjugacy classes & character table

4172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 593);