Finite Group Databasebeta

#108×D439 #43243648

order28096
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D439

Splittings

Fitting#108×C439 ⋊ C2
SylowC439 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D439
commutatorC4×C439C22×C4
FrattiniC2×C4C22×D439
Fitting#108×C439C2
socleC2×C439C2×C4⋊C4
prime radicalC22×D439Q8
cosocleC2×C4×C439C23
hypercenter#108D439
hypocenterC439C2×#108
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7024

Conjugacy classes & character table

3094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 593);