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H(5,𝔽2)×#1044 #72221791

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C5

Aliases

direct productH(5,𝔽2)×#1044

Splittings

FittingC52×H(5,𝔽2) ⋊ C4
SylowC52 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2C24×#1044
commutator, socleC2×C52C24×C4
FittingC52×H(5,𝔽2)C4
prime radicalH(5,𝔽2)×C5⋊D5C2
cosocleC2×C5⋊D5C25
hypercenterH(5,𝔽2)#1044
hypocenterC52C4×H(5,𝔽2)
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ H(5,𝔽2)

4218 conjugacy classes of subgroups; only the 890 normal subgroups are shown.

normal subgroups only

This group has 4218 conjugacy classes of subgroups — too many to draw. Only its 890 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

170 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.