Finite Group Databasebeta

#108×D41 #14580380

order2624
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D41

Splittings

Fitting#108×C41 ⋊ C2
SylowC41 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D41
commutatorC4×C41C22×C4
FrattiniC2×C4C22×D41
Fitting#108×C41C2
socleC2×C41C2×C4⋊C4
prime radicalC22×D41Q8
cosocleC2×C4×C41C23
hypercenter#108D41
hypocenterC41C2×#108
LCSG ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 656

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 593);