Finite Group Databasebeta

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C5⋊D5×D231 #37528711

order23100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5⋊D5×D231

Splittings

Fitting, socle, derived, HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×D33
HallC7×C11 ⋊ D3×C5⋊D5
HallC3×C52 ⋊ C2×D77
HallC3×C11 ⋊ D7×C5⋊D5
SylowC52 ⋊ C2×D231
HallC3×C7 ⋊ D11×C5⋊D5
SylowC11 ⋊ D21×C5⋊D5
SylowC7 ⋊ C5⋊D5×D33
SylowC3 ⋊ C5⋊D5×D77

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7×C11
UCSC1

320 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 522);