Finite Group Databasebeta

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M16×#11924078 #34037089

order18752
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×#11924078

Splittings

FittingM16×C293 ⋊ C4
SylowC293 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC4C22×#11924078
commutator, socleC2×C293C2×C42
FittingM16×C293C4
prime radicalC22×D293C2×C4
cosocleC4×D293C23
hypercenterM16#11924078
hypocenterC293C4×M16
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C4 ◁ M16

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2344

Conjugacy classes & character table

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

Relationships

maximal subgroup of#100×#11924078, #101×#11924078, #104×#11924078, …
maximal normal subgroup of#100×#11924078, #101×#11924078, #104×#11924078, …
maximal quotient ofM16×#14556880, #49173983, #49173986, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 1509);