Finite Group Databasebeta

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#1043×#3811 #72259420

order14400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#1043×#3811

Splittings

FittingC22×C32×C52 ⋊ C22×C4
HallC32×C52 ⋊ C2×C4×D4
SylowC52 ⋊ C4×#3811
SylowC32 ⋊ C2×D4×#1043

Subgroups

subgroupG/H
center, FrattiniC2C2×D32×#1043
commutator, socleC2×C32×C52C23×C4
FittingC22×C32×C52C22×C4
prime radicalC5⋊D5×#3811C2
cosocleC2×C32×C5⋊D5C24
hypercenterC22D32×#1043
hypocenterC32×C52C2×C4×D4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C2 ◁ C22

7760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 300

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#1043×#3811
maximal normal subgroup ofC2×#1043×#3811
maximal quotient ofC2×#1043×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.