Finite Group Databasebeta

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C2×#1043×#3811 #72260043

order28800
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#1043×#3811

Splittings

FittingC23×C32×C52 ⋊ C22×C4
HallC32×C52 ⋊ C22×C4×D4
SylowC52 ⋊ C2×C4×#3811
SylowC32 ⋊ C22×D4×#1043

Subgroups

subgroupG/H
centerC22C2×D32×#1043
commutatorC2×C32×C52C24×C4
FrattiniC2C22×D32×#1043
FittingC23×C32×C52C22×C4
socleC22×C32×C52C23×C4
prime radicalC2×C5⋊D5×#3811C2
cosocleC2×C32×C5⋊D5C25
hypercenterC23D32×#1043
hypocenterC32×C52C22×C4×D4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C22 ◁ C23

45896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.