Finite Group Databasebeta

#108×D421 #41002884

order26944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D421

Splittings

Fitting#108×C421 ⋊ C2
SylowC421 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D421
commutatorC4×C421C22×C4
FrattiniC2×C4C22×D421
Fitting#108×C421C2
socleC2×C421C2×C4⋊C4
prime radicalC22×D421Q8
cosocleC2×C4×C421C23
hypercenter#108D421
hypocenterC421C2×#108
LCSG ▷ C4×C421 ▷ C2×C421 ▷ C421
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6736

Conjugacy classes & character table

2968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 593);