Finite Group Databasebeta

#108×C22⋊D79 #34306519

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#108×C22⋊D79

Splittings

FittingC22×#108×C79 ⋊ C2
SylowC79 ⋊ D4×#108

Subgroups

subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC22×#108×C79C2
socleC22×C79C22×C4⋊C4
prime radicalC22×C22⋊D79Q8
cosocleC22×C4×C79C24
hypercenterC22×#108D79
hypocenterC79D4×#108
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#108

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

2254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 187818);