Finite Group Databasebeta

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C3×(C5⋊D5)⋊D77 #37528623

order23100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×(C5⋊D5)⋊D77

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C22
derived, HallC52×C7×C11 ⋊ C22×C3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ D52
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C3×D52
HallC3×C52 ⋊ C2×D77
HallC3×C11 ⋊ (C5⋊D5)⋊D7
SylowC52 ⋊ C2×C3×D77
HallC3×C7 ⋊ (C5⋊D5)⋊D11
SylowC11 ⋊ C3×(C5⋊D5)⋊D7
SylowC7 ⋊ C3×(C5⋊D5)⋊D11

Subgroups

subgroupG/H
center, hypercenterC3(C5⋊D5)⋊D77
commutator, cosocle, hypocenterC52×C7×C11C22×C3
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 2310

Conjugacy classes & character table

1644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 434);