Finite Group Databasebeta

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C22×D293⋊C8 #34037200

order18752
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D293⋊C8
unambiguous semidirect productD293⋊(C22×C8)

Splittings

derived, SylowC293 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#11924078
commutator, hypocenterC293C23×C8
FrattiniC2C23×#11924078
FittingC22×C4×C293C4
socleC23×C293C2×C4
prime radicalC23×D293C4
cosocleDic293C24
LCSG ▷ C293
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×(C2×#11924078)⋊C8, #49174446, #49174452, …
maximal normal subgroup ofC2×(C2×#11924078)⋊C8, #49174446, #49174452, …
maximal quotient ofC22×C4×#14556880, C2×C4×D293⋊C8, C2×D293⋊(C22⋊C8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 1620);