Finite Group Databasebeta

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C2×#626×#1043 #72259638

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

Aliases

direct productC2×#626×#1043

Splittings

HallC32×C52 ⋊ C2×C4×D4
SylowC52 ⋊ C2×C4×#626
SylowC32 ⋊ C2×D4×#1043

Subgroups

subgroupG/H
center, hypercenterC22D32×#1043
commutatorC2×C32×C52C23×C4
FrattiniC2C2×D32×#1043
Fitting, socleC22×C32×C52C22×C4
prime radicalC2×C5⋊D5×#626C2
cosocleC2×C32×C5⋊D5C24
hypocenterC32×C52C2×C4×D4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C22

7760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

Relationships

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.