Finite Group Databasebeta

#108×D577 #49147993

order36928
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D577

Splittings

Fitting#108×C577 ⋊ C2
SylowC577 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D577
commutatorC4×C577C22×C4
FrattiniC2×C4C22×D577
Fitting#108×C577C2
socleC2×C577C2×C4⋊C4
prime radicalC22×D577Q8
cosocleC2×C4×C577C23
hypercenter#108D577
hypocenterC577C2×#108
LCSG ▷ C4×C577 ▷ C2×C577 ▷ C577
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9232

Conjugacy classes & character table

4060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 593);