Finite Group Databasebeta

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C2×Q8×#11924078 #34037194

order18752
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#11924078
unambiguous semidirect productD293⋊(C4×Q8)

Splittings

FittingC2×Q8×C293 ⋊ C4
SylowC293 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#11924078
commutatorC2×C293C23×C4
FrattiniC2C23×#11924078
FittingC2×Q8×C293C4
socleC22×C293C22×C4
prime radicalC22×D293C23
cosocleC2×D293C24
hypercenterC2×Q8#11924078
hypocenterC293C2×C4×Q8
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

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

Relationships

maximal subgroup of#101×#11924078, #103×#11924078, #49174558, …
maximal normal subgroup of#101×#11924078, #103×#11924078, #49174558, …
maximal quotient ofC2×C4⋊C4×#11924078, C4×Q8×#11924078, C2×#34037078, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 1614);