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(C5⋊D5)⋊D23 #14556293

order2300
isoclinismisoclinic class of (C5⋊D5)⋊D23
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C5⋊D5)⋊D23
unambiguous semidirect productD115⋊D5

Splittings

Fitting, socle, derived, HallC52×C23 ⋊ C22
SylowC52 ⋊ C2×D23
SylowC23 ⋊ D52

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C23C22
LCSG ▷ C52×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 230

Polycyclic presentation:

2^2,5^2,23|c^a=c^4,e^a=e^22,c^b=c^4,d^b=d^4

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×(C5⋊D5)⋊D23, D115⋊D35, (C5⋊D5)⋊D161, …
maximal normal subgroup ofC7×(C5⋊D5)⋊D23, (C5⋊D5)⋊AGL(1,𝔽23), C11×(C5⋊D5)⋊D23, …
maximal quotient ofC7×(C5⋊D5)⋊D23, D115⋊D35, (C5⋊D5)⋊D161, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2300, 31);