Finite Group Databasebeta

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C3×C8×AGL(1,𝔽25) #72223567

order14400
automorphism?
homologyAbelianization (H1) = C32×C82 · Schur multiplier (H2) = C3×C8

Aliases

BorelB(2,𝔽25)
direct productC3×C8×AGL(1,𝔽25)

Splittings

FittingC3×C52×C8 ⋊ C3×C8
derived, SylowC52 ⋊ C32×C82
HallC8×#6053 ⋊ C32
HallC3×C52⋊C3 ⋊ C82

Subgroups

subgroupG/H
center, hypercenterC3×C8AGL(1,𝔽25)
commutator, hypocenterC52C32×C82
FrattiniC4C2×C3×AGL(1,𝔽25)
FittingC3×C52×C8C3×C8
socleC2×C3×C52C3×C4×C8
prime radicalC2×C3×(C5⋊D5)⋊C3C42
cosocleC4×#1043C22×C32
LCSG ▷ C52
UCSC1 ◁ C3×C8

488 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.