Finite Group Databasebeta

← Prev (#72221352) Next (#72221354) →

C2×#104×#1043 #72221353

order6400
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#104×#1043

Splittings

FittingC2×C52×#104 ⋊ C4
SylowC52 ⋊ C2×C4×#104

Subgroups

subgroupG/H
centerC2×C4D4×#1043
commutatorC4×C52C22×C42
FrattiniC2×C4C23×#1043
FittingC2×C52×#104C4
socleC22×C52C4×C22⋊C4
prime radicalC2×#41×C5⋊D5C22
cosocleC2×C4×C5⋊D5C24
hypercenterC2×#104#1043
hypocenterC52C2×C4×#104
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

7512 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#453×#1043, C2×#444×#1043
maximal normal subgroup ofC2×#453×#1043, C2×#444×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.