Finite Group Databasebeta

← Prev (#72223261) Next (#72223263) →

#1043×#1705 #72223262

order12800
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C8

Aliases

direct product#1043×#1705

Splittings

FittingC52×#1705 ⋊ C4
SylowC52 ⋊ C4×#1705

Subgroups

subgroupG/H
centerC22#127×#1043
commutatorC42×C52C23×C4
FrattiniC42C23×#1043
FittingC52×#1705C4
socleC22×C52C4×#127
prime radical#127×C5⋊D5C23
cosocleC42×C5⋊D5C24
hypercenter#1705#1043
hypocenterC52C4×#1705
LCSG ▷ C42×C52 ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42 ◁ #1705

7888 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.