Finite Group Databasebeta

#108×D419 #41000405

order26816
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D419

Splittings

Fitting#108×C419 ⋊ C2
SylowC419 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D419
commutatorC4×C419C22×C4
FrattiniC2×C4C22×D419
Fitting#108×C419C2
socleC2×C419C2×C4⋊C4
prime radicalC22×D419Q8
cosocleC2×C4×C419C23
hypercenter#108D419
hypocenterC419C2×#108
LCSG ▷ C4×C419 ▷ C2×C419 ▷ C419
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6704

Conjugacy classes & character table

2954 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 593);